Demophon is a name that refers to two different characters in Greek mythology. One of them was the son of King Celeus and Queen Metanira. During the goddess Demeter's quest to find her daughter Persephone, who had been kidnapped by Hades, she ended up in Celeus' palace in Eleusis, having taken the form of an old woman named Doso. Celeus was very hospitable to the old woman and asked her to nurse his sons, Demophon and Triptolemus. Demeter, grateful for Celeus' hospitality, decided to secretely give immortality to Demophon by annointing him with ambrosia and then burning his mortal spirit in the family hearth. One night, though, Metanira saw what was happening and screamed in freight, thus angering Demeter. So, she stopped the ritual.

The other Demophon was a king of Athens, son of Theseus and Phaedra. Along with Acamas, his brother, they freed their grandmother Aethra when she was captured by the Dioscuri. Demophon also fought in the Trojan War. On his return home from the war, he stopped in Thrace and fell in love with the daughter of the local king, called Phyllis, and ended up marrying her. However, he left the next day of the wedding saying he would return as soon as possible. Phyllis gave him a casket and told him to open it only if he was certain he would never again return to Thrace. Demophon eventually went to Cyprus and forgot about Phyllis, who died of grief waiting for her husband's return. One day though, Demophon decided to open the casket out of curiosity, and looked at something so terrible that trying to escape, he fell off his horse and onto his sword. Another account has it that Demophon returned to Thrace but Phyllis, already dead, had transformed into a barren almond tree; when Demophon touched it though, it started to blossom.